Question

A 60 W bulb is placed at a distance of 4m from you. The bulb is emitting light of wavelength 600 nm uniformly in all directions. In 0.1 s, how many photons enter your eye if the pupil of the eye is having a diameter of 2 mm? [Take $hc=1240eV-nm]$

• A. $2.84\times {10}^{12}$
• B. $2.84\times {10}^{11}$
• C. $9.37\times {10}^{11}$
• D. $6.48\times {10}^{11}$

Answer 1

The correct option is B $2.84\times {10}^{11}$

$Power,P=60WWavelength,\lambda =600nm=600\times {10}^{-9}mtime,t=0.1sIntensity,I=\frac{P}{A}=\frac{60}{4\pi r^2}=\frac{60}{4\pi \left(16\right)}=0.3W/㎡also,I=\frac{nhc}{\lambda 4\pi r^2}wherenisthenumberofphotons,\therefore n=\frac{I\lambda 4\pi r^{2}t}{hc}=\frac{0.3\times 600\times {10}^{-9}\times 4\times \pi \times 16\times 0.1}{6.6\times {10}^{-34}\times 3\times {10}^8}\to n=1.83\times {10}^{19}Numberofphotonsenteringtheeye=n\times ratioofareofpupilofeyeandareaofincidence=n\times \frac{\pi \times 1mm\times 1mm}{4\pi \times \left(4^2\right)}=1.83\times {10}^{19}\times \frac{{10}^{-6}}{64}=2.84\times {10}^{11}$